Problem: Simplify the following expression: $ p = -9 + \dfrac{-6x + 4}{x + 9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{x + 9}{x + 9}$ $ \dfrac{-9}{1} \times \dfrac{x + 9}{x + 9} = \dfrac{-9x - 81}{x + 9} $ Therefore $ p = \dfrac{-9x - 81}{x + 9} + \dfrac{-6x + 4}{x + 9} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{-9x - 81 - 6x + 4}{x + 9} $ $p = \dfrac{-15x - 77}{x + 9}$